# Full-dimensional (12D) variational vibrational states of CH$_4\cdot$F$^-$: interplay of anharmonicity and tunneling

## TL;DR

This study presents full-dimensional variational vibrational calculations of CH$_4$·F$^-$, revealing small tunneling splittings, significant anharmonicity, and the necessity of 12D treatment for accurate vibrational states and tunneling phenomena.

## Contribution

It provides the first full-dimensional (12D) vibrational analysis of CH$_4$·F$^-$, demonstrating the importance of anharmonicity and tunneling effects using advanced computational methods.

## Key findings

- Tunneling splittings are smaller than 0.02 cm$^{-1}$.
- Single-well models are insufficient due to anharmonicity.
- Tunneling splittings increase with vibrational excitation.

## Abstract

The complex of a methane molecule and a fluoride anion represents a 12-dimensional (12D), four-well vibrational problem with multiple large-amplitude motions, which has challenged the quantum dynamics community for years. The present work reports vibrational band origins and tunneling splittings obtained in a full-dimensional variational vibrational computation using the GENIUSH program and the Smolyak quadrature scheme. The converged 12D vibrational band origins and tunneling splittings confirm complementary aspects of the earlier full- and reduced-dimensionality studies: (1) the tunneling splittings are smaller than 0.02 cm$^{-1}$; (2) a single-well treatment is not sufficient (except perhaps the zero-point vibration) due to a significant anharmonicity over the wells; and thus, (3) a full-dimensional treatment appears to be necessary. The present computations extend to a higher energy range than earlier work, show that the tunneling splittings increase upon vibrational excitation of the complex, and indicate non-negligible `heavy-atom' tunneling.